Availability Analysis and Preventive Maintenance Planning for Systems with General Time Distributions

Steady-state availability is one of the most important performance measures for repairable systems. To improve the steady-state availability of such systems, preventive maintenance (PM) models have been extensively studied. However, these models assume that the distributions of the system lifetime and maintenance duration are exponential. In practice, the probabilistic characteristics of different systems and maintenance actions are so broad making the exponential distribution an inappropriate model. This paper seeks to determine the optimal PM strategy that maximizes the steady-state availability of a system involving general probability distributions. Specifically, PM is scheduled periodically, and a certain number of imperfect maintenance (IM) actions are carried out before each replacement. We develop state-transition equations involving general probability distributions using a supplementary variable method. The stationary distribution is calculated by solving the system of linear equations, through which the steady-state availability of the system is obtained. We prove the existence of the optimal combination of the number of IM actions before each replacement and the scheduled PM interval. Numerical examples are presented to illustrate the effectiveness of our proposed method in handling such practical maintenance problems.